In this paper, we have analized the behavior of the functional ϱ, associated to the bi weight correlation estimator – ϱ –, assuming the sampled population has a bivariate normal distribution. The purpose is to verify if the estimator ϱ is an unbiased estimator of the correlation coefficient ρ. The results show ϱ > ρ when ρ 0, y ϱ= 0 when ρ = 0. This results indicate ϱ is not an unbiased estimator of the correlation coefficient.